Abstract
Navigating and understanding surroundings requires judging sizes and poses of objects. The length of the retinal image of an object lying on the ground depends on the angle of the pose, being smallest when the object is pointing towards or away from the observer. Estimating veridical length requires correcting for the foreshortening, which could be done by back-transforming the perspective projection function. Maruya and Zaidi (JOV 2020) showed that observers’ size estimates for different poses of objects on the ground can be explained by the optimal back-transform function but for elevation of observation or slant of the object confounded with projected length. We now investigate the case of sloped objects with one end raised above the ground. Rectangular parallelepipeds of 6, 8, 10 cm oriented in 16 poses from 0º-337.5º and slopes of 22.5º and 45º, with and without naturalistic shading, were viewed in proper perspective (Viewpoint elevation 15º, distance 1.0m). Six observers estimated lengths using an adjustable measuring stick. Observers made veridical estimates at most poses, thus correcting for projective distortions, but underestimated sizes of objects pointing towards them, especially for the 22.5º slope and to a lesser extent overestimated sizes of objects pointing away for the 45º. Estimates deviated more from veridical for longer objects, but there was no appreciable effect of shading. The optimal perspective correction function was derived from the retinal projection for each slope of the object. Varying the slope angle changed the shape of the correction function appreciably, because foreshortening decreases as the difference from the viewing elevation progresses toward 90º. Observers’ size corrections matched the optimal function for almost all poses, suggesting they use the correct stored geometric function, but deviated for poses pointing towards or away from observers, possibly because of the paucity of visual information for slope angle in these poses.